Problem: Simplify the following expression: $\sqrt{125} + \sqrt{80}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{125} + \sqrt{80}$ $= \sqrt{25 \cdot 5} + \sqrt{16 \cdot 5}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{5} + \sqrt{16} \cdot \sqrt{5}$ $= 5\sqrt{5} + 4\sqrt{5}$ Finally, simplify by combining the terms. $= ( 5 + 4 )\sqrt{5} = 9\sqrt{5}$